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107 LearnersLast updated on September 24, 2025
GCF of 90 and 135
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 90 and 135.
What is the GCF of 90 and 135?
The greatest common factor of 90 and 135 is 45. The largest divisor of two or more numbers is called the GCF of the numbers.
If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 90 and 135?
To find the GCF of 90 and 135, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 90 and 135 by Using Listing of Factors
Steps to find the GCF of 90 and 135 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. Factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135.
Step 2: Now, identify the common factors of them Common factors of 90 and 135: 1, 3, 5, 9, 15, 45.
Step 3: Choose the largest factor The largest factor that both numbers have is 45. The GCF of 90 and 135 is 45.
GCF of 90 and 135 Using Prime Factorization
To find the GCF of 90 and 135 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 90: 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5 Prime Factors of 135: 135 = 3 × 3 × 3 × 5 = 3³ × 5
Step 2: Now, identify the common prime factors The common prime factors are: 3 × 3 × 5 = 3² × 5
Step 3: Multiply the common prime factors 3² × 5 = 9 × 5 = 45. The Greatest Common Factor of 90 and 135 is 45.
GCF of 90 and 135 Using Division Method or Euclidean Algorithm Method
Find the GCF of 90 and 135 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 135 by 90 135 ÷ 90 = 1 (quotient), The remainder is calculated as 135 − (90×1) = 45 The remainder is 45, not zero, so continue the process
Step 2: Now divide the previous divisor (90) by the previous remainder (45) Divide 90 by 45 90 ÷ 45 = 2 (quotient), remainder = 90 − (45×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 90 and 135 is 45.
Common Mistakes and How to Avoid Them in GCF of 90 and 135
Finding the GCF of 90 and 135 seems simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 90, students may mention 8, which is incorrect.
To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one.
To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers.
However, it does not affect the GCF, but it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with multiples. In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number.
To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 90 and 135 Examples
Problem 1
A chef has 90 apples and 135 oranges. He wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 90 and 135 GCF of 90 and 135 3² × 5 = 9 × 5 = 45. There are 45 equal groups 90 ÷ 45 = 2 135 ÷ 45 = 3 There will be 45 groups, and each group gets 2 apples and 3 oranges.
Explanation
As the GCF of 90 and 135 is 45, the chef can make 45 groups.
Now divide 90 and 135 by 45.
Each group gets 2 apples and 3 oranges.
Problem 2
A school has 90 red chairs and 135 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 90 and 135 3² × 5 = 9 × 5 = 45. So each row will have 45 chairs.
Explanation
There are 90 red and 135 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 90 and 135.
There will be 45 chairs in each row.
Problem 3
A gardener has 90 meters of red rope and 135 meters of blue rope. She wants to cut both ropes into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 90 and 135 The GCF of 90 and 135 3² × 5 = 9 × 5 = 45. The rope is 45 meters long.
Explanation
For calculating the longest length of the rope, first we need to calculate the GCF of 90 and 135, which is 45.
The length of each piece of the rope will be 45 meters.
Problem 4
A carpenter has two wooden planks, one 90 cm long and the other 135 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 90 and 135 3² × 5 = 9 × 5 = 45. The longest length of each piece is 45 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 90 cm and 135 cm, respectively.
We have to find the GCF of 90 and 135, which is 45 cm.
The longest length of each piece is 45 cm.
Problem 5
If the GCF of 90 and ‘a’ is 45, and the LCM is 270. Find ‘a’.
The value of ‘a’ is 135.
Explanation
GCF × LCM = product of the numbers
45 × 270 = 90 × a
12150 = 90a
a = 12150 ÷ 90
= 135
FAQs on the Greatest Common Factor of 90 and 135
1.What is the LCM of 90 and 135?
2.Is 90 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 135?
5.Are 90 and 135 prime numbers?
Important Glossaries for GCF of 90 and 135
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 6 are 6, 12, 18, 24, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
